Explanation Given information: The length of the shaded area is 4 ft. The height of the shaded area is 16 ft. Calculation: Show the area of the differential element as in Figure 1. Using Figure 1, Express the parabolic value of y . y = ( 4 − x 1 / 2 ) 2 Compute the area of the element. d A = y d x Here, the area of element is dA . Substitute ( 4 − x 1 / 2 ) 2 for y . d A = ( 4 − x 1 / 2 ) 2 d x = ( x − 8 x 1 / 2 + 16 ) d x Compute the centroid of the differential element along the x axis using the formula. x ˜ = x Determine the location of the center of gravity of the homogeneous rod along the x axis ( x ¯ ) using the relation. x ¯ = ∫ A x ˜ d A ∫ A d A (1) Conclusion: Apply the limits from 0 ft to 4 ft and substitute x for x ˜ and ( x − 8 x 1 / 2 + 16 ) d x for dA in Equation (1). x ¯ = ∫ 0 4 ft ( x ) ( x − 8 x 1 / 2 + 16 ) d x ∫ 0 4 ft ( x − 8 x 1 / 2 + 16 ) d x (2) Calculate the numerator part from Equation (2). ∫ 0 4 ft ( x ) ( x − 8 x 1 / 2 + 16 ) d x = [ ( x 3 3 − 16 5 x 5 / 2 + 8 x 2 ) ] 0 4 ft = [ ( ( 4 ft ) 3 3 − 16 5 ( 4 ft ) 5 / 2 + 8 ( 4 ft ) 2 ) ] = 21

Statics and Mechanics of Materials, Student Value Edition (5th Edition)

5th Edition

ISBN: 9780134382890

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related t…

Videos

Question

Chapter 6.1, Problem 15P

To determine

Find the centroid x¯ of the parabolic shaded area.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.1, Problem 14P

Chapter 6.1, Problem 16P

Students have asked these similar questions

I submitted the below question and received the answer i copied into this question as well. Im unsure if it is correct, so looking for a checkover. i am stuck on the part tan-1 (0.05) = 0.04996 radians. Just unsure where the value for the radians came from. Just need to know how they got that answer and how it is correct before moving on to the next part. If any of the below information is wrong, please feel free to give me a new answer or an entire new explanation. An Inclining experiment done on a ship thats 6500 t, a mass of 30t was moved 6.0 m transvesly causing a 30 cm deflection in a 6m pendulum, calculate the transverse meta centre height. Here is the step-by-step explanation: Given: Displacement of the ship (W) = 6500 tonnes = 6500×1000=6,500,000kg Mass moved transversely (w) = 30 tonnes=30×1000=30,000kg The transverse shift of mass (d) = 6.0 meters Pendulum length (L) = 6.0 meters Pendulum deflection (x) = 30 cm = 0.30 meters Step 1: Formula for Metacentric Height…

Answer the assignment question, expert only

A 1 inch rod diameter B 3/4 inch rod diameter C 1/2 inch rod diameter D 3/8 inch rod diameter

Chapter 6 Solutions

Statics and Mechanics of Materials, Student Value Edition (5th Edition)

Ch. 6.1 - In each case, use the element shown and specify...Ch. 6.1 - Prob. 1FP Ch. 6.1 - Determine the centroid (x,y) of the area. Prob....Ch. 6.1 - Determine the centroid y of the area. Prob. F63 Ch. 6.1 - Locate the center of gravity x of the straight rod...Ch. 6.1 - Prob. 5FP Ch. 6.1 - Locate the centroid z of the homogeneous solid...Ch. 6.1 - Locate the centroid x of the area. Prob. 61 Ch. 6.1 - Locate the centroid of the area. Prob. 62 Ch. 6.1 - Locate the centroid x of the area. Probs. 63/4

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Find the centroid x ¯ of the parabolic shaded area.

Solution Summary: The author explains how to find the centroid of the parabolic shaded area.

Concept explainers

Videos

Find the centroid x¯ of the parabolic shaded area.

Want to see the full answer?

Chapter 6 Solutions